If COM of a system of particles lies at the origin of the coordinate system then

x - coordinate of all the particles may be positive

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x - coordinate of all the particles may be negative

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x - coordinate of all the particles may be zero

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y - coordinate of all the particles may be positive

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Solution

The correct option is C x - coordinate of all the particles may be zero
As COM lies the origin
$X_{C M} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}} = 0$
$m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3} = 0$
So, x - coordinate of all the particles may be zero.

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If COM of a system of particles lies at the origin of the coordinate system then

The correct option is C x - coordinate of all the particles may be zero As COM lies the origin XCM=m1x1+m2x2+m3x3m1+m2+m3=0 m1x1+m2x2+m3x3=0 So, x - coordinate of all the particles may be zero.

The correct option is C x - coordinate of all the particles may be zero
As COM lies the origin
$X_{C M} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}} = 0$
$m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3} = 0$
So, x - coordinate of all the particles may be zero.